MinT - Best Known (137−34, 137, s)-Nets in Base 9

Best Known (137−34, 137, s)-Nets in Base 9

(137−34, 137, 940)-Net over F₉ — Constructive and digital

Digital (103, 137, 940)-net over F₉, using

1 times m-reduction [i] based on digital (103, 138, 940)-net over F₉, using
- (u,Â u+v)-construction [i] based on
  1. digital (19, 36, 200)-net over F₉, using
    - trace code for nets [i] based on digital (1, 18, 100)-net over F₈₁, using
      - net from sequence [i] based on digital (1, 99)-sequence over F₈₁, using
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 1 and N(F) ≥ 100, using
        a function field by SÃ©mirat [i]
  2. digital (67, 102, 740)-net over F₉, using
    - trace code for nets [i] based on digital (16, 51, 370)-net over F₈₁, using
      - net from sequence [i] based on digital (16, 369)-sequence over F₈₁, using
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 16 and N(F) ≥ 370, using
        a function field by GarcÃa and Quoos [i]

(137−34, 137, 15076)-Net over F₉ — Digital

Digital (103, 137, 15076)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(137−34, 137, large)-Net in Base 9 — Upper bound on s

There is no (103, 137, large)-net in base 9, because

32 times m-reduction [i] would yield (103, 105, large)-net in base 9, but
- mutually orthogonal hypercube bound [i]